A General Form Of Precise Asymptotics For The Dependent Sequences

The definition ofρ-mixing was advanced in 1960 and the definition of NA was in the 1980s. Form then on, many scholars have discussed their limit properties in weak convergence, maximal inequality and the complete convergence. There are many results now which are mostly derived from the i.i.d, sequences. In this paper I try to discuss its further limit properties in maximal partial sum.In chapter one, we introduce the definition ofρ-mixing sequence, NA(negative association)and the main results which were proved by the scholars before. Especially, Zhang L.X.(2004)proved the complete convergence in NA sequences; Feng Y.C., Wang Y.B.(2004) proved precise asymptotics of partial sums forⅡD and NA sequences; Zhao Y.X. et al. (2007)gives the precise rate in theρ-mixing sequeces.In chapter two we derive a general form of precise rate in the limit properties for maximal partial sum for NA sequences, by combining the methods in Zhang L.X. (2004)and Feng Y.C., Wang Y.B.(2004).In chapter three we derive a general form of precise rate in the in the law of the iterated logarithm for maximal partial sum in theρ-mixing sequences, by combining the methods in Huang W. et al.(2003) and Zhao Y.X. et al. (2007).